Problem: For a given input value $m$, the function $f$ outputs a value $n$ to satisfy the following equation. $7m+2=6n-5$ Write a formula for $f(m)$ in terms of $m$. $f(m)=$
Solution: $f(m)$ expresses $n$ as a function of $m$. To arrive at a correct formula, all we have to do is solve the equation for $n$. $ \begin{aligned}7m+2&=6n-5\\\\ 7m+7&=6n\\\\ \dfrac{7m}{6}+\dfrac{7}{6}&=n\end{aligned}$ Therefore, this formula expresses $n$ as a function of $m$ : $ f(m)=\dfrac{7}{6}m+\dfrac{7}{6}$